earthquake hazard modelers

Abstract: Earthquake sequences are stochastic on two separated timescales: the seismic waves of any individual earthquake propagate over seconds to minutes, while the earthquakes themselves arrive as a sparse, self-exciting occurrence process, with inter-event intervals from seconds to months. Respecting both scales in one training objective is the open challenge. Foundation models (FMs) for seismic waveforms instead import their learning targets from audio and vision, where every target is computed from a single fixed-length window. Such a window holds one realization of the wave propagation (an earthquake trace), never the occurrence process that decides when earthquakes happen. We develop nine model designs sharing one Mamba encoder-decoder, trained on a fixed corpus of 3M windows, varying the self-supervised objective, quantization bottleneck and mixer; the two key comparisons are architecture-matched, varying the objective alone. Each checkpoint is evaluated frozen on three downstream tasks. Varying the target redistributes downstream skill rather than raising it, and no checkpoint wins everywhere. Adding masking pressure to our strongest classifier re-specializes it rather than making it a generalist: it gains 6.9 points of few-shot P-wave picking precision and loses 9.6 points of few-shot classification accuracy. By the standard imported from language and vision, these models are feature extractors rather than FMs. Controls on capacity, architecture, and domain proximity do not explain why skill moves rather than rises. Against task-specific baselines the advantage is regime-dependent: our checkpoints beat them few-shot on classification and ground-motion prediction, and trail them on full data. We argue the binding constraint is the target, and that settling the question requires a learning target defined across events, the timescale that makes seismicity stochastic in the first place.

Abstract: Full waveform inversion (FWI) estimates subsurface velocity from seismic recordings, but its ill-posedness and nonlinearity make accurate reconstruction strongly dependent on initialization and prior information. Diffusion posterior sampling provides a learned geological prior, yet directly coupling its denoiser to the nonlinear wave solver can yield unreliable physical guidance. We propose Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity to the diffusion prior through a Gaussian bridge. The physical state is refined by waveform fitting regularized by the denoised velocity, and in turn guides the reverse diffusion process. This formulation separates the wave-equation and denoiser gradients while preserving conventional FWI initialization and accumulated optimization history. On four OpenFWI families, PSG's terminal denoised estimates outperform classical and diffusion-based baselines under clean and missing-trace acquisitions and maintain strong structural recovery under measurement noise. Repeated stochastic runs preserve the dominant geological structures, with ensemble variability concentrated near geological interfaces and positively associated with local inversion error. A frozen OpenFWI-trained prior further supports inversion of the larger Marmousi, Overthrust, and BP2004 Salt models, recovering complex geological structures without retraining.